If choking it makes it run better, the problem is lean mixture. That could be caused by restriction upstream of the carburetor, carburetor malfunction, or mixture dilution downstream of the carburetor. Perhaps the simplest thing that could cause it, is a problem with the fuel tank air vent. A partial vacuum in the fuel tank causes lean mixture but may not prevent starting (it may or may not make starting difficult). A split in a fuel hose, or a blockage in the fuel pickup in the tank, might also be responsible. I had a chainsaw once with a split in the fuel pickup hose - that was a pain to find.
If the mixture adjustments have no effect, that seems to indicate that the problem is upstream of them, and fuel supply limitations are swamping the effect of the carburetor adjustments. A fuel pump problem could still be the cause, but on the face of it, downstream mixture dilution is unlikely to be causing the difficulty. In other words, I wouldn't be going to the crankcase seals as the first suspects.
